Definition of Continued fraction. Meaning of Continued fraction. Synonyms of Continued fraction

Here you will find one or more explanations in English for the word Continued fraction. Also in the bottom left of the page several parts of wikipedia pages related to the word Continued fraction and, of course, Continued fraction synonyms and on the right images related to the word Continued fraction.

Definition of Continued fraction

Continued fraction
Fraction Frac"tion, n. [F. fraction, L. fractio a breaking, fr. frangere, fractum, to break. See Break.] 1. The act of breaking, or state of being broken, especially by violence. [Obs.] Neither can the natural body of Christ be subject to any fraction or breaking up. --Foxe. 2. A portion; a fragment. Some niggard fractions of an hour. --Tennyson. 3. (Arith. or Alg.) One or more aliquot parts of a unit or whole number; an expression for a definite portion of a unit or magnitude. Common, or Vulgar, fraction, a fraction in which the number of equal parts into which the integer is supposed to be divided is indicated by figures or letters, called the denominator, written below a line, over which is the numerator, indicating the number of these parts included in the fraction; as 1/2, one half, 2/5, two fifths. Complex fraction, a fraction having a fraction or mixed number in the numerator or denominator, or in both. --Davies & Peck. Compound fraction, a fraction of a fraction; two or more fractions connected by of. Continued fraction, Decimal fraction, Partial fraction, etc. See under Continued, Decimal, Partial, etc. Improper fraction, a fraction in which the numerator is greater than the denominator. Proper fraction, a fraction in which the numerator is less than the denominator.
Continued fraction
Continued Con*tin"ued, p. p. & a. Having extension of time, space, order of events, exertion of energy, etc.; extended; protracted; uninterrupted; also, resumed after interruption; extending through a succession of issues, session, etc.; as, a continued story. ``Continued woe.' --Jenyns. ``Continued succession.' --Locke. Continued bass (Mus.), a bass continued through an entire piece of music, while the other parts of the harmony are indicated by figures beneath the bass; the same as thorough bass or figured bass; basso continuo. [It.] Continued fever (Med.), a fever which presents no interruption in its course. Continued fraction (Math.), a fraction whose numerator is 1, and whose denominator is a whole number plus a fraction whose numerator is 1 and whose denominator is a whole number, plus a fraction, and so on. Continued proportion (Math.), a proportion composed of two or more equal ratios, in which the consequent of each preceding ratio is the same with the antecedent of the following one; as, 4 : 8 : 8 : 16 :: 16 : 32.

Meaning of Continued fraction from wikipedia

- another simple or continued fraction. Depending on whether this iteration terminates with a simple fraction or not, the continued fraction is finite or infinite...
- A simple or regular continued fraction is a continued fraction with numerators all equal one, and denominators built from a sequence { a i } {\displaystyle...
- Gauss's continued fraction is a particular class of continued fractions derived from hypergeometric functions. It was one of the first analytic continued fractions...
- In mathematics, an infinite periodic continued fraction is a simple continued fraction that can be placed in the form x = a 0 + 1 a 1 + 1 a 2 + 1 ⋱ a...
- common fraction. But every number, including π, can be represented by an infinite series of nested fractions, called a simple continued fraction: π = 3...
- In number theory, the continued fraction factorization method (CFRAC) is an integer factorization algorithm. It is a general-purpose algorithm, meaning...
- continued fractions, Euler's continued fraction formula is an identity connecting a certain very general infinite series with an infinite continued fraction...
- The Rogers–Ramanujan continued fraction is a continued fraction discovered by Rogers (1894) and independently by Srinivasa Ramanujan, and closely related...
- truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one. Decimal...
- irreducible quadratic). A simple continued fraction is a continued fraction where the denominator is 1. The simple continued fraction expansion of Champernowne's...